1994final - SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO...

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Unformatted text preview: SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO MATA26Y April 19, 1995 FINAL EXAMINATION 1. Evaluate the following integrals exactly if they exist. [4] (a) Z sin x √ 2 + cos x dx [4] (b) Z ∞ 2 1 4 + z 2 dz [4] (c) Z 1 a x + a- x dx , where a is a positive real number. [4] (d) Z e 1 9 x 2 ln xdx [4] 2. (a) Evaluate F ( x ) = Z x π/ 2 ( t + 1)cos2 tdt . [3] (b) Verify your answer to (a) by differentiating your expression for F ( x ). [4] 3. (a) State the first and secondversion of the Fundamental Theorem of Calculus. [4] (b) The function F ( x ) = R √ 9- x 2 e- t 2 2 dt has domain [- 3 , 3]. What are the values of F at the endpoints of that interval? Where is F decreasing/increasing? [9] 4. Determine the area of the region(s) enclosed by the curves y = x 2 and y = p | x | . Make a sketch! [4] 5. (a) State the trapezoidal rulefor numerical integration with error bound. [6] (b) The function f ( x ) = √ 1 + x 4 takes on the following values t 1 4 1 2 3 4 1 5 4 3 2 7 4 2 f ( t ) 1 1 . 002 1...
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1994final - SCARBOROUGH CAMPUS UNIVERSITY OF TORONTO...

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